"act of putting (a vehicle) in a certain place," 1915, verbal noun from park (v.). Parking lot "plot of ground used for parking vehicles" is from 1920; parking ticket "notification of a parking violation" attested by 1925; parking meter "device to measure the time allowed for parking" is by 1935. Parking brake "brake used to hold a parked vehicle in place" is recorded from 1927.
1812, "to arrange military vehicles in a park," from park (n.) in a limited sense of "enclosure for guns, wagons, horses, provisions, etc." (attested from 1680s). General non-military meaning "to put (a vehicle) in a certain place" is first recorded 1844. Related: Parked; parking. Park-and-ride is from 1966.
Oh the torn up ticket stubs
From a hundred thousand mugs
Now washed away with dead dreams in the rain;
And the car-park's going up
And they're pulling down the pubs
And it's just another bloody rainy day
[The Pogues, "White City," 1989]
"device or instrument for measuring," abstracted 1832 from gasometer (in English from 1790), etc., from French -mètre, used in combinations, from Latin metrum "measure" or cognate Greek metron "measure" (from PIE root *me- (2) "to measure").
English already had meter "person who measures, official who checks that measured quantities are correct" (late 14c., c. 1300 as a surname, agent noun from unrelated mete (v.)), which might have influenced this word. As short for parking meter from 1960. Meter maid "woman police official who patrols metered parking sites" is recorded by 1957, meter reader as a job is by 1872 (originally in reference to gas meters).